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- # Copyright (c) 2012 Manfred Moitzi
- # License: MIT License
- from typing import List, Sequence
- from .bezier import bernstein_basis
- Vector = Sequence[float]
- class BezierSurface:
- def __init__(self, defpoints: List[List[Vector]]):
- """
- BezierSurface constructor
- Args:
- defpoints: defpoints is matrix (list of lists) of m rows and n columns.
- [ [m1n1, m1n2, ... ], [m2n1, m2n2, ...] ... ]
- each element is a 3D point (x, y, z) tuple or list
- """
- self._defpoints = defpoints
- self.nrows = len(defpoints)
- self.ncols = len(defpoints[0])
- def appoximate(self, usegs: int, vsegs: int) -> List[List[Vector]]:
- stepu = 1.0 / float(usegs)
- stepv = 1.0 / float(vsegs)
- result = [[None] * self.ncols] * self.nrows # type: List[List[Vector]]
- for u_index in range(usegs + 1):
- u = stepu * u_index
- for v_index in range(vsegs + 1):
- v = stepv * v_index
- result[u_index][v_index] = self.get_point(u, v)
- return result
- def get_point(self, u: float, v: float) -> Vector:
- """ u, v in range [0.0, 1.0].
- """
- point = [0.0, 0.0, 0.0]
- for irow in range(self.nrows):
- rowbasis = bernstein_basis(self.nrows, irow, u)
- row = self._defpoints[irow]
- for col in range(self.ncols):
- colbasis = bernstein_basis(self.ncols, col, v)
- for axis in (0, 1, 2):
- point[axis] += row[col][axis] * rowbasis * colbasis
- return point
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